Solve sqrt{24^2/2.4012*10^-7}

$$\sqrt { \frac { 24 ^ { 2 } } { 2.4012 \times 10 ^ { - 7 } } }$$

Evaluate

$$\frac{400000\sqrt{6670}}{667}\approx 48977.55199783$$

Solution Steps

Calculate 24 to the power of 2 and get 576.

$$\sqrt{\frac{576}{2.4012\times 10^{-7}}}$$

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\sqrt{\frac{576}{2.4012\times \frac{1}{10000000}}}$$

Multiply 2.4012 and \frac{1}{10000000} to get \frac{6003}{25000000000}.

$$\sqrt{\frac{576}{\frac{6003}{25000000000}}}$$

Divide 576 by \frac{6003}{25000000000} by multiplying 576 by the reciprocal of \frac{6003}{25000000000}.

$$\sqrt{576\times \frac{25000000000}{6003}}$$

Multiply 576 and \frac{25000000000}{6003} to get \frac{1600000000000}{667}.

$$\sqrt{\frac{1600000000000}{667}}$$

Rewrite the square root of the division \sqrt{\frac{1600000000000}{667}} as the division of square roots \frac{\sqrt{1600000000000}}{\sqrt{667}}.

$$\frac{\sqrt{1600000000000}}{\sqrt{667}}$$

Factor 1600000000000=400000^{2}\times 10. Rewrite the square root of the product \sqrt{400000^{2}\times 10} as the product of square roots \sqrt{400000^{2}}\sqrt{10}. Take the square root of 400000^{2}.

$$\frac{400000\sqrt{10}}{\sqrt{667}}$$

Rationalize the denominator of \frac{400000\sqrt{10}}{\sqrt{667}} by multiplying numerator and denominator by \sqrt{667}.

$$\frac{400000\sqrt{10}\sqrt{667}}{\left(\sqrt{667}\right)^{2}}$$

The square of \sqrt{667} is 667.

$$\frac{400000\sqrt{10}\sqrt{667}}{667}$$

To multiply \sqrt{10} and \sqrt{667}, multiply the numbers under the square root.

$$\frac{400000\sqrt{6670}}{667}$$